Israeli tanks ride along the border of Israel and the Gaza Strip, Sunday. Escalating their ground offensive, Israeli troops backed by tanks and warplanes battled Hamas militants in a crowded neighborhood of Gaza City early Sunday. (AP Photo/Tsafrir Abayov

Palestinian health officials reported at least 65 people killed as air and artillery strikes echoed across the city for hours. They put the number of displaced at 35,000, with at least 435 people killed in the nearly two-week conflict.

Israeli military casualties spiked in the fighting, with 13 killed Sunday, raising the total number of dead soldiers to 18. Two civilians also have died in mortar and rocket attacks.

Diplomats' efforts to end the violence continued, as U.N. chief Ban Ki-moon headed to the region to try to revive cease-fire efforts. U.S. Secretary of State John Kerry said he expects to come to the Middle East in coming days and that he support's Egypt's call for an immediate cease-fire, rejected last week by Hamas. The Islamic militants say they want guarantees that Gaza's border blockade will be eased before agreeing to stop fighting.

Sunday's battle in Gaza City's Shijaiyah neighborhood was the deadliest so far in Israel's 3-day-old ground offensive, which followed 10 days of heavy airstrikes on targets linked to Gaza's Hamas rulers. Israel has said it sent thousands of troops into Gaza to destroy Hamas rocket launchers and tunnels dug by the Islamic militants to sneak into Israel.

The Israeli military said 8 percent of more than 1,700 rockets fired at Israel since July 8 came from Shijaiyah and that its troops faced heavy resistance there.

Residents of the neighborhood said Israeli tanks entered after midnight and fired heavily.

"The gate of hell has opened, and shrapnel came through the windows," Shijaiyah resident Jawad Hassanain said by phone. He said he and his family sought shelter in a nearby building after their house shook from the explosions.

"All you could hear is heavy bombardment, the smell of fire and the smell of death," he said.

After daybreak, dozens of wounded from Shijaiyah were rushed to Gaza's central Shifa Hospital. Frantic parents carried children bloodied by shrapnel, and the emergency room quickly overflowed, forcing doctors to treat some patients on mattresses in a hallway.

During a brief Red Cross-brokered lull, paramedics entered the neighborhood to retrieve the dead, pulling bodies from the rubble of homes. Dozens of houses over several blocks were destroyed or badly damaged, a scene reminiscent of Israel's last major incursion into Gaza more than five years ago when large areas near the border with Israel were devastated.

On late Sunday afternoon, Gaza rescue workers searching Shijaiyah for bodies heard the faint voice of a woman coming from under the rubble of a house.

Rescue workers said the area was dangerous and that they would not be able to dig her out in time.

Palestinian health officials said at least 65 people were killed and 288 wounded in Shijaiyah, bringing the overall Palestinian toll since July 8 to 435 dead and some 3,000 wounded. Close to half of the dead were killed since the start of the ground offensive.

Lt. Col. Peter Lerner, a military spokesman, said the military met a "huge" level of resistance from Hamas militants in Shijaiyah, with anti-tank missiles, rocket-propelled grenades and automatic-weapons fired from houses and buildings.

He said that so far, 10 tunnel access shafts were found in the area.

Lerner said Shijaiyah had been a main rocket launching area and that residents were warned ahead of the offensive to leave the area.

"We are mobilizing in order to strike Hamas where it hurts," he said.

Israel says Hamas' network of tunnels is a highly-developed web which links rocket building, maintenance and launching sites and stretches well into Israel.

Speaking to CNN, Israeli Prime Minister Benjamin Netanyahu said Israel is only targeting militants in its campaign.

"All civilian casualties are unintended by us, but intended by Hamas. They want to pile up as many civilian dead as they can ... it's gruesome," Netanyahu said. "They use telegenically dead Palestinians for their cause. They want the more dead the better."

Israel has also targeted homes of Hamas leaders, warning they would pay a high price.

Among those killed in Shijaiyah were a son, daughter-in-law and two grandchildren of Khalil al-Haya, a senior leader of the group. They were killed at the time of dawn prayers, Health Ministry official Ashraf al-Kidra said. Hamas' military wing said the cause of death as an airstrike on the family. Israel's military had no immediate comment.

Thousands of residents began fleeing Shijaiyah after daybreak, including a woman in a wheelchair who waved a white flag. Columns of smoke rose from the neighborhood as the sound of shelling echoed from inside.

Gaza's Health Ministry later said 35,000 people fled Sunday's fighting.

Some residents tried to find refuge with relatives or at U.N. schools. Some 81,000 Palestinians are already staying in United Nations shelters, according to UNRWA, the U.N. refugee agency for Palestinians.

The number of people who have fled their homes has more than quadrupled since the start of Israel's ground operation and the agency said it planned to open more schools.

The heavy fighting came as Ban headed to Qatar to try to push stalled cease-fire efforts forward.

He was set to meet Western-backed Palestinian President Mahmoud Abbas in the Gulf state, Abbas' spokesman said. Abbas also plans to meet Hamas' top leader Khaled Mashaal.

Hamas last week rejected an Egyptian call on both sides to halt hostilities, saying it first wants guarantees that Israel and Egypt will significantly ease their border blockade of Gaza, which has been ruled by the Islamic militant group since 2007.

Hamas has sought involvement of other countries, such as Qatar, in any cease-fire negotiations. The militant group is deeply distrustful of Egypt's rulers, who last year deposed a Hamas-friendly government in Cairo.